Fuller equation

Di = 4.64 X 10 m /s (estimated using Wilke-Chang equation. Chapter 8) = 18.6 X 10 m /s (estimated using Fuller equation. Chapter 8)... 

Fuller s equation, applied for the estimation of the coefficient of diffusion of a binary gas mixture, at a pressure greater than 10 bar, predicts values that are too high. As a first approximation, the value of the coefficient of diffusion can be corrected by multiplying it by the compressibility of the gas /... 

Unfortunately, in most cases not all the available information on a reaction is given in the reaction equation in a publication, and even less so in reaction databases. To obtain a fuller picture of the reaction that was performed, the text describing the experimental procedure in the publication or a lab journal) would have to be consulted. Reaction products that are considered as trivial, such as water, alcohol, ammonia, nitrogen, etc., are generally not included in the reaction equation or mentioned in the text describing the experimental work. This poses serious problems for the automatic identification of the reaction center. It is highly desirable to have the full stoichiometry of a reaction specified in the equation. 

Unlike simple deflections or accelerations of ions in magnetic and electric fields (Chapter 25), the trajectory of an ion in a quadrupolar field is complex, and the equations of motion are less easy to understand. Accordingly, a simplified version of the equations is given here, with a fuller discussion in the Appendix at the end of this chapter. 

Fuller-Schettler-Giddings The parameters and constants for this correlation were determined by regression analysis of 340 experimental diffusion coefficient values of 153 binary systems. Values of X Vj used in this equation are in Table 5-16. 

A method, proposed more recently by FULLER, SCHETTLER and GlDDlNGSf8 . is claimed to give an improved correlation. In this approach the values of the diffusion volume have been modified to give a better correspondence with experimental values, and have then been adjusted arbitrarily to make the coefficient in the equation equal to unity. The method does contain some anomalies, however, particularly in relation to the values of V for nitrogen, oxygen and air. Details of this method are given in Volume 6. 

The equation developed by Fuller et al. (1966) is easy to apply and gives reliable estimates ... 

The temperature dependence of the conductivity can be described by the classical Arrhenius equation a = a"cxp(-E7RT), where E is the activation energy for the conduction process. According to the Arrhenius equation the lna versus 1/T plot should be linear. However, in numerous ionic liquids a non-linearity of the Arrhenius plot has been reported in such a case the temperature dependence of the conductivity can be expressed by the Vogel-Tammann-Fuller (VTF) relationship a = a°cxp -B/(T-T0), ... 

Fuller-Kinyon pump, 11 378 Fuller-Schettler-Giddings diffusivity equation, 15 674 Fuller s earth, 6 666, 686... 

From the equation (1) p decrease at Df reduction follows, as always Djmacromolecular coil inner regions and results to the fuller chemical transformations, i.e., to conversion degree Q increase. Besides, it is known [4], that at macromolecular coil formation by irreversible aggregation mechanisms in its central part... 

Equation 17.33 has a limited application. A fuller discussion of adsorption from gas mixtures can be found in the literature(31619 20). 

Concentrated Solution "Theory. For an electrolyte with three species, it is as simple and more rigorous to use concentrated solution theory. Concentrated solution theory takes into account all binary interactions between all of the species. For membranes, this was initially done by Bennion ° and Pintauro and Bennion. ° They wrote out force balances for the three species, equating a thermodynamic driving force to a sum of frictional interactions for each species. As discussed by Fuller,Pintauro and Bennion also showed how to relate the interaction parameters to the transport parameters mentioned above. The resulting equations for the three-species system are... 

Recently, Ray et al. (1991b) reported the vapor pressure of glycerol at 298 K to be 0.0223 Pa. Equation (109) yields a value of 0.0138 Pa at that temperature. It appears that the correlation of Tang and Munkelwitz underpredicts the vapor pressure near room temperature because of the procedure used to determine the constants in the equation. The approximation written as Eq. (110) is not sufficiently accurate to permit its application over a wide range of temperatures. As shown by Fuller et al. (1966), data for numerous low-molecular-weight binary systems agree with the approximation that Dij is proportional to An exponent between 1.75 and 2 would be a better... 

Or some fuller description of the primary structure may be given such as that in Equation 2.2 for three repeat units of PVC where the particular geometry around each chiral carbon is given ... 

If a salt undergo hydrolysis in solution according to the equation M--t-X + H O M-+ OH -P X + H, and the adsorbing agent selectively adsorbs the acid H X the hydrolysis will evidently proceed further until equilibrium is attained. In the case of Fuller s earth it may be considered that the earth selectively adsorbs hydrochloric acid leaving an alkaline solution of caustic soda. This view of promoted hydrolysis by adsorption is at variance with the hypothesis of ionic interchange and can only be tested by careful analysis of the solution to find out whether ionic interchange has taken place or no. 

Formation of a bond between two heteroatoms is also of considerable utility in the synthesis of sulfur-containing polyheteroatom systems. Reaction of 1,5-dinucleophiles with electrophilic sulfur reagents such as thionyl chloride or sulfur dichloride leads directly to the heterocycles (e.g. equation 55). A fuller discussion of these types of reaction is given in Chapter 2.28. 

A fuller explanation of the BMPT theory, and their equations defining liner collapse jet formation is found in Cook (Ref 2)... 

In order to gain a fuller insight into the nature of any exchange reaction, it is necessary to determine a second rate constant k, representing the initial rate of disappearance of the light hydrocarbon C H in percentage per unit time. This may be obtained by using the empirical first-order equation... 

The ail viscosity can be found in Table 1.2, Appendix I, where we find that the viscosity at 644 K is about 3.1 X 10 5 kg/m s. The Fuller—Schettler—Giddings equation is proposed for the determination of the diffusion coefficient of nonpolar gases in binary mixtures at... 

The Chapman-Enskog theory (Chapman and Cowling, 1970) is a model which is positioned between the two approaches, the empirical relation by Fuller et al. (Eq. 18-44) and the theoretically stringent Equation 18-43. This theory improves the absolute size of the expression by taking into account the individual sizes and interactions of the diffusing molecules. However, the numerical values obtained with the model by Fuller et al. (Eq. 18-44) are still better than both the Chapman-Enskog theory and Eq. 18-43. 

A brief description of this procedure is abstracted from the fuller treatment of Henley and Seader (1981). The MESH equations (13.182)-(13.186) in terms of mol fractions are transformed into equations with molal flow rates of individual components in the liquid phase ltJ and vapor phase vif as the primary variables. The relations between the transformed variables are in this list ... 

Reprint P (= [277]) is the last of three dialogue papers, the others being [145] = J, App. 1., and [204] = J, App. 2. There is some overlap in matter, and the description of the logistical equation here is much fuller than it was in the first dialogue simply because much more was known about it in 1993 than had been in 1977. A paper designed for a literary audience, having a... 

Diffuse reflection from powder sample is a complex combination of transmission, internal and external reflections, and scattering. It is dependent on the particle size, absorption and refractive indices of the studied material. The case of proper prepared powder diffuse reflection R carries the information primarily about the transmission spectrum of the sample (Willey 1976 Fuller and Griffiths 1978). The traditional method of the absorption spectra (K) calculation on the base of the diffuse reflection R is the Kubelka-Munk equation K = (1 - R)2S/2Rc, where S is the scattering coefficient, concentration of the studied material is c = 1 in our case. 

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